Question 1 of 3 · No calculator needed
Which conclusion follows deductively from the assumption that n is divisible by 6?
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
OCR · Mathematics B (MEI) · A LevelMathematics,
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Question 2 of 3 · No calculator needed
Rationalise 4/(3 - √5).
Multiply by (3 + √5)/(3 + √5). The denominator is 9 - 5 = 4, so the expression becomes 4(3 + √5)/4 = 3 + √5.
Question 3 of 3 · No calculator needed
How many real solutions does x⁴ + 1 = 3x² have?
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
These tiles show your answers to three questions. They are a starting point, not a mastery score or grade prediction.
Proof
Correct answer: n is divisible by 3
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
Algebra
Correct answer: 3 + √5
Multiply by (3 + √5)/(3 + √5). The denominator is 9 - 5 = 4, so the expression becomes 4(3 + √5)/4 = 3 + √5.
Graphs
Correct answer: 4
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
For parents: look at the explanation together. A correct answer is encouraging; a missed answer gives you something specific to work on. Broader practice over time is needed to understand progress.
YOUR TOPIC MAP
23 areasFind your starting point.
01Algebra
Specification reference: H640 Algebra Ma1-Ma14
Algebra requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algebra requires. Keep exact values until the final step and check signs, units and reasonableness.
02Calculus
Specification reference: H640 Calculus Mc1-Mc32
Calculus requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Calculus requires. Keep exact values until the final step and check signs, units and reasonableness.
03Coordinate geometry
Specification reference: H640 Coordinate geometry Mg1-Mg8
Coordinate geometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Coordinate geometry requires. Keep exact values until the final step and check signs, units and reasonableness.
04Data presentation and interpretation
Specification reference: H640 Data presentation and interpretation Md1-Md18
Data presentation and interpretation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Data presentation and interpretation requires. Keep exact values until the final step and check signs, units and reasonableness.
05Exponentials and logarithms
Specification reference: H640 Exponentials and logarithms Me1-Me11
Exponentials and logarithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Exponentials and logarithms requires. Keep exact values until the final step and check signs, units and reasonableness.
06Forces
Specification reference: H640 Forces MF1-MF12
Forces requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Forces requires. Keep exact values until the final step and check signs, units and reasonableness.
07Functions
Specification reference: H640 Functions Mf1-Mf8
Functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Functions requires. Keep exact values until the final step and check signs, units and reasonableness.
08Graphs
Specification reference: H640 Graphs MC1-MC9
Graphs requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Graphs requires. Keep exact values until the final step and check signs, units and reasonableness.
09Kinematics in one dimension
Specification reference: H640 Kinematics Mk1-Mk8
Kinematics in one dimension requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Kinematics in one dimension requires. Keep exact values until the final step and check signs, units and reasonableness.
10Kinematics in two dimensions
Specification reference: H640 Kinematics Mk9-Mk12
Kinematics in two dimensions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Kinematics in two dimensions requires. Keep exact values until the final step and check signs, units and reasonableness.
11Models and quantities
Specification reference: H640 Models and quantities Mp31-Mp35
Models and quantities requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Models and quantities requires. Keep exact values until the final step and check signs, units and reasonableness.
12Newton's laws of motion
Specification reference: H640 Newton's laws Mn1-Mn7
Newton's laws of motion requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Newton's laws of motion requires. Keep exact values until the final step and check signs, units and reasonableness.
13Numerical methods
Specification reference: H640 Numerical methods Mn1-Mn12
Numerical methods requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Numerical methods requires. Keep exact values until the final step and check signs, units and reasonableness.
14Probability distributions
Specification reference: H640 Probability distributions MR1-MR13
Probability distributions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability distributions requires. Keep exact values until the final step and check signs, units and reasonableness.
15Probability
Specification reference: H640 Probability Mu1-Mu12
Probability requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability requires. Keep exact values until the final step and check signs, units and reasonableness.
16Projectiles
Specification reference: H640 Projectiles My1-My5
Projectiles requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Projectiles requires. Keep exact values until the final step and check signs, units and reasonableness.
17Proof
Specification reference: H640 Proof Mp1-Mp3
Proof requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Proof requires. Keep exact values until the final step and check signs, units and reasonableness.
18Rigid bodies
Specification reference: H640 Rigid bodies MF13-MF16
Rigid bodies requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Rigid bodies requires. Keep exact values until the final step and check signs, units and reasonableness.
19Statistical sampling
Specification reference: H640 Sampling Ms1-Ms5
Statistical sampling requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statistical sampling requires. Keep exact values until the final step and check signs, units and reasonableness.
20Sequences and series
Specification reference: H640 Sequences and series Ms1-Ms14
Sequences and series requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Sequences and series requires. Keep exact values until the final step and check signs, units and reasonableness.
21Statistical hypothesis testing
Specification reference: H640 Statistical hypothesis testing Mh1-Mh12
Statistical hypothesis testing requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statistical hypothesis testing requires. Keep exact values until the final step and check signs, units and reasonableness.
22Trigonometry
Specification reference: H640 Trigonometry Mt1-Mt21
Trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
23Vectors
Specification reference: H640 Vectors Mv1-Mv10
Vectors requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vectors requires. Keep exact values until the final step and check signs, units and reasonableness.
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OCR · Mathematics B (MEI) · A Level · Mathematics · H640
Version 3, October 2025, current checked 2026-08-27
Source checked: 2026-08-27. The current official specification controls assessment requirements and option choices.
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Yes. This page offers three original questions from three different skills on this exact course. Each answer has an explanation, followed by a sample heatmap showing what was correct and what to revisit. No account is needed, and taster answers are not saved.
What does the three-question heatmap tell a parent?
It shows the outcome of these three answers and gives a specific skill to discuss or practise next. It is not a full assessment, a mastery score or a grade prediction. Broader practice over time is needed to understand progress.
What does the OCR · Mathematics B (MEI) A Level Mathematics route cover?
LearningP currently maps 23 assessed areas for specification H640. The visible topic map below is derived from the verified route; the current official specification remains controlling.
How many LearningP questions support this route?
The verified source bank contains 266 original LearningP question records for this route. Every mapped area meets the current publication minimum and passed the latest blocker and review audit.
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No. LearningP uses official specifications and assessment materials to map content and demand, while its practice questions and explanations are independently authored.
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No. LearningP reports practice evidence, coverage, strengths and gaps. It does not guarantee or automatically predict examination outcomes.
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Use the official OCR · Mathematics B (MEI) specification and assessment-resource pages linked on this page, together with information supplied by the learner’s school.
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